Euclidean Bus Mobility and Route Optimization, A Comparison

Routes in Queens, New York City, NY

Introduction

This project uses stplanr transport modeling package to design an optimal transport route for bus or cycle routes in New York City. Stplanr is a transport planning visualization R package that can be used to plan transit networks, in addition to transit planning elements such as identifying transit catchment areas, origin/destination data and ride frequency visualizations, among others. In their white paper, the devlopers of stplanr call for an accountable, transparent and democratized transit planning system that doesn’t rely on proprietary and often vastly different data sources and data processing softwares. Although the package can visualize a whole host of data, this project will focus on comparing direct desire lines or “Euclidean” routes (as the crow flies), existing bus networks and stplanr’s optimized routes. To wit: this can map the efficiency of the bus routes compared to the most direct route possible if there were no built environment factors in the way.

Methods

To adequately compare desire lines, bus routes, and the most efficient routes with the current street network, this project will require at minimum three data sources. Each of these will be sourced separately and overlaid onto each other:

• Data Source: leaflet data for basemap
  • Methods: This can be sourced directly into R by installing the leaflet package. It provides an interactive background map that can be used to overlay other spatial data, and the options can be toggled on and off for ease of use.
  • Source: Leaflet for R
• Data Source: OpenStreetMap (OSMR) data for transit data, either bus or cycle routes, this is used as the route vector data.
  • Methods: This can be sourced directly into R by installing the package. You may need to rationalize different projection systems to make sure they overlay correctly.
    
  • Source: Mapping with OpenStreetMap in R
• Data Source: NYC Open Data for Bus Shelter locations
  Despite significant searching, there is no comprehensive bus stop dataset, so the project will focus on bus stop shelters, which are mapped via NYC Open Data. I used Bus Shelters as there would be thousands upon thousands of bus stops in NYC, and this would be too computationally intensive to process.
  
  • Methods: This can be brought into R as a CSV file. Each bus stop shelter has longitude and latitude coordinates that align with leaflet and OpenStreetMap projections.
    
  • Source: NYC Bus Stop Shelters, NYC Transit analysis
• Data Source: NYC Open Data for NYC Borough Boundaries
  • Methods: This can be brought into R as a shapefile. This will provide the basemap boundary for NYC to ensure all data is within the city limits.
  • Source: NYC Borough Boundaries, Department of City Planning

Data Preparation

• Load the necessary R packages for spatial data manipulation and visualization (e.g., ggmap, dplyr, stplanr, osmdata, sf, leaflet).
• Import the NYC basemap shapefile and bus shelter CSV data into R.
• Convert the bus shelter data into an sf object with appropriate coordinate reference system (CRS).

Terms:

• Desire Lines: Straight lines connecting origin and destination points, representing the most direct path between them.
• Euclidean: Direct points between shelters. “As the crow flies”.
• OSRM: Open Street Routing Machine, a routing engine that uses Open Street Map data to calculate routes, shortest routes, travel times, and can be used to make travel time maps, distance routing for car, bike and walking.

Interactive Map:

#install libraries
library(ggmap)
library(dplyr)
library(stplanr)
library(osmdata)
library(sf)
library(tidyverse)
library(leaflet)
library(purrr)
library(kableExtra)
library(scales)

#SHAPEFILES AND MAP
bbox <- c(left = -73.96, bottom = 40.54, right = -73.70, top = 40.81)
#create bounding box for NYC

nyc_map <- "data/"#

#nyc basemap, downloaded from nyc open data. source: https://search.r-project.org/CRAN/refmans/ptools/html/nyc_bor.html

nyc_sf <- st_read(nyc_map, quiet =TRUE)
#bring in nyc_map as a sf

shelters_sf <- read_csv("data/Bus_Stop_Shelter_20251020.csv")
#NOTE: REPLACE WITH DATA WHEN USING QUARTO!
#this brings in the bus stop shelter information. source: https://data.cityofnewyork.us/Transportation/Bus-Stop-Shelters/qafz-7myz

shelters_sf_fix <- st_as_sf(shelters_sf, coords = c("Longitude","Latitude"), crs = 4326)
#convert to sf object with the correct coordinate reference system

osmdata::set_overpass_url("https://overpass-api.de/api/interpreter")
#set overpass url for open street maps

osm_data <- opq(bbox = bbox) %>%
  add_osm_feature(key = "highway", value = c("primary","secondary")) %>%
  osmdata_sf()
#import data for primary and secondary highways from open street maps

# STPLANR

shelters_sf_fix <- shelters_sf_fix %>%
  mutate(id = paste0("S", row_number()))
#add ID column for origin-destination pairs so they have a corresponding number

flow_all <- expand.grid(o = shelters_sf_fix$id, #create origin
                        d = shelters_sf_fix$id, #create destination
                        stringsAsFactors = FALSE) %>% #make sure they aren't factors
  filter(o != d) %>% # this remove self-pairs so O is not D
  mutate(trips = 1) %>% #add trip count of 1 for each pair
  sample_n(50) #sample 50 random paris to avoid blowing up the computer

desire_lines_all <- od2line(flow_all, zones = shelters_sf_fix, zone_code = "id") #use od2line function to create desire lines (euclidean) for all pairs

shelter_coords <- shelters_sf_fix %>%
  st_coordinates() %>%
  as.data.frame() %>%
  bind_cols(id = shelters_sf_fix$id)
#extract coordinates and bind with ID column

route_single <- function(o_id, d_id) { #function to create a single route between origin and destination
  o <- shelter_coords %>% filter(id == o_id) 
  #filter to get origin coordinates
  d <- shelter_coords %>% filter(id == d_id)
  #filter to get destination coordinates

  r <- try(route_osrm(from = c(o$X, o$Y),
                      to   = c(d$X, d$Y)), silent = TRUE)
#use try to catch errors  (e.g., no route found)
  if (inherits(r, "try-error")) return(NULL)
#if route found, return the route
  return(r)
}

routes_list <- purrr::map2(flow_all$o, flow_all$d, route_single)
#create routes for all origin-destination pairs using the route_single function
routes_list <- routes_list[!sapply(routes_list, is.null)]
#remove any NULL results (failed routes)
routes_sf <- do.call(rbind, routes_list)
#combine all routes into a single sf object

#BELOW: create a comparison between route lengths and desire line lengths & calculate means and percent change

routes_projection <- st_transform(routes_sf, 32618)
desire_projection <- st_transform(desire_lines_all, 32618)
#ensures the correct, projected shapefile for computation not mapping

route_length <- st_length(routes_projection)
desire_length <- st_length(desire_projection)
#compute lengths

route_length <- as.numeric(route_length)
desire_length <- as.numeric(desire_length)
#convert lengths to numeric values

lengths_tbl <- tibble(
  route_m  = route_length,
  desire_m = desire_length,
  origin = flow_all$o,
  destination = flow_all$d
)
#create tibble to compare lengths in the final map w/ IDs

lengths_tbl_print <- tibble(
  route_m  = comma(round(route_length)),
  desire_m = comma(round(desire_length)),
  origin = flow_all$o,
  destination = flow_all$d
)
#tidy data for later printing in a kable

mean_route <- mean(route_length, na.rm = TRUE)
mean_desire <- mean(desire_length, na.rm = TRUE)
#calculate means for both route and desire lengths

percent_change <- ((mean_route - mean_desire) / mean_desire) * 100
#calculate percent change 

mean_lengths <- data.frame(
  type = c("Route Length", "Desire Line Length"),
  mean_length_m = c(round(mean_route), round(mean_desire)))

#put these into a data frame, rounded to whole numbers


mean_lengths <- mean_lengths %>%
  mutate(
    mean_length_km = mean_length_m / 1000,
    percent_change = c(percent_change, NA)
  )
#add km conversion and percent change to the data frame, i converted to KM for ease of computation (ie: dividing by 1,000)

mean_lengths_print <- mean_lengths %>%
  mutate(
    mean_length_km = comma(round(mean_length_m / 1000)),
    percent_change = comma(round(percent_change))
  )
#tidy data for later printing in a kable

#LEAFLET PREP
nyc_leaflet  <- st_transform(nyc_sf, 4326)
roads_leaflet <- st_transform(osm_data$osm_lines, 4326)
desire_leaflet <- st_transform(desire_lines_all, 4326)
routes_leaflet <- st_transform(routes_sf, 4326)
#transform all data to WGS84 for leaflet mapping

desire_leaflet_popup <- paste0(
  "<b>Desire Line</b><br/>",
  "Origin: ", desire_leaflet$o, "<br/>",
  "Destination: ", desire_leaflet$d, "<br/>",
  "Desire Line Distance: ", round(lengths_tbl$desire_m / 1000), " km"
)
#create popup info for desire lines for interactive map
  
routes_leaflet_popup <- paste0(
  "<b>OSRM Route</b><br/>",
  "Origin: ", desire_leaflet$o, "<br/>",
  "Destination: ", desire_leaflet$d, "<br/>",
  "Route Distance: ", round(lengths_tbl$route_m / 1000), " km<br/>"
)
#create popup info for routes for interactive map

pal_desire <- colorNumeric(
  palette = "viridis",
  domain  = lengths_tbl$desire_m
)
#create color palette for desire lines based on distance

pal_routes <- colorNumeric(
  palette = "inferno",
  domain  = lengths_tbl$route_m
)
#create color palette for routes based on distance

selected_ids <- unique(c(flow_all$o, flow_all$d))
#get unique IDs of sampled shelters

selected_shelters <- shelters_sf_fix %>% 
  filter(id %in% selected_ids)
#filter shelters to only those that were sampled

#LEAFLET MAP
leaflet() %>%
  addProviderTiles("CartoDB.Positron") %>%
  
  addPolygons(data = nyc_leaflet,
              color = "black", weight = 3,
              fillOpacity = 0.1,
              group = "NYC Boundary") %>%
  # Add OSM roads w/ positron background
  
  addPolylines(
    data = desire_leaflet,
    color = pal_desire(lengths_tbl$desire_m),
    weight = 3,
    opacity = 0.7,
    popup = desire_leaflet_popup,
    group = "Desire Lines"
  ) %>%
  
  addPolylines(
    data = routes_leaflet,
    color = pal_routes(lengths_tbl$route_m),
    weight = 3,
    opacity = 0.8,
    popup = routes_leaflet_popup,
    group = "OSRM Routes"
  ) %>%
  
  addLegend(
    pal = pal_desire,
    values = lengths_tbl$desire_m,
    title = "Desire Line Distance (m)",
    position = "bottomright",
    group = "Desire Lines"
  ) %>%
  #add a legend for desire lines
  addLegend(
    pal = pal_routes,
    values = lengths_tbl$route_m,
    title = "OSRM Route Distance (m)",
    position = "bottomleft",
    group = "OSRM Routes"
  ) %>%
  #add a legend for osrm routes

    addCircleMarkers(data = shelters_sf_fix,
                   color = "blue",
                   radius = 1,
                   popup = ~id,
                   group = "Bus Shelters") %>%
  #add all bus shelters
  addCircleMarkers(
    data = selected_shelters,
    color = "purple",
    radius = 6,
    fillOpacity = 0.9,
    group = "Sampled Shelters"
  ) %>%
  #add sampled bus shelters with purple markers
  addLayersControl(
    overlayGroups = c("NYC Boundary", "Sampled Shelters",
                      "Desire Lines", "OSRM Routes",
                      "Bus Shelters"),
    options = layersControlOptions(collapsed = FALSE)
  )

Tables:

mean_lengths_print %>%
  kable(col.names = c("Type", "Mean Length (m)", "Mean Length (km)", "Percent Change (%)"),
        caption = "Mean Lengths of OSRM Routes vs Desire Lines") %>%
  kable_styling(full_width = FALSE, position = "left")

Mean Lengths of OSRM Routes vs Desire Lines

Type	Mean Length (m)	Mean Length (km)	Percent Change (%)
Route Length	17860	18	21
Desire Line Length	14820	15	NA

lengths_tbl_print %>%
  kable(col.names = c("Route Length (m)", "Desire Line Length (m)", "Origin ID", "Destination ID"),
        caption = "Comparison of Route Lengths and Desire Line Lengths for Sampled Origin-Destination Pairs") %>%
  kable_styling(full_width = FALSE, position = "left")

Comparison of Route Lengths and Desire Line Lengths for Sampled Origin-Destination Pairs

Route Length (m)	Desire Line Length (m)	Origin ID	Destination ID
27,014	24,234	S656	S2356
15,823	13,618	S247	S1792
7,740	7,128	S845	S1300
31,900	30,500	S3219	S1057
17,033	13,924	S615	S2355
14,802	12,871	S2432	S1517
28,293	20,968	S1155	S2261
12,050	10,704	S125	S470
7,296	5,190	S2228	S1827
6,300	4,986	S319	S572
10,956	8,804	S1468	S162
25,778	20,727	S1208	S700
5,203	4,417	S1991	S1522
20,473	18,374	S907	S1672
6,942	5,491	S1053	S1232
5,331	4,110	S1028	S1223
24,112	22,097	S3227	S1516
9,347	6,096	S839	S2205
16,067	13,753	S2705	S788
21,181	18,646	S1551	S27
2,595	2,268	S750	S739
23,943	20,683	S1867	S2802
6,937	5,778	S1740	S2082
18,390	17,004	S2931	S2101
30,206	6,145	S29	S3195
43,611	39,475	S1381	S3254
21,297	18,497	S1478	S2860
18,180	17,012	S31	S1686
36,747	31,279	S862	S926
19,801	17,714	S2895	S817
14,537	13,511	S546	S746
28,727	21,128	S947	S3164
28,059	22,398	S595	S2455
6,403	5,388	S2133	S96
795	776	S2988	S2329
16,704	15,239	S60	S2700
14,380	11,593	S964	S2588
6,159	4,483	S1809	S2896
29,767	25,151	S700	S1073
23,550	21,978	S2165	S3269
11,918	8,643	S2206	S1416
40,755	33,680	S3248	S3028
15,243	13,084	S2318	S17
1,654	975	S1883	S1350
7,441	6,849	S267	S39
48,625	41,065	S3152	S3367
12,063	10,613	S1738	S2123
25,513	21,091	S545	S1212
12,146	10,088	S2664	S227
13,195	10,752	S1876	S2559

Results

The mean route length for the optimized routes for this particular sample run is 17.86 km, while the mean Euclidean desire line length is 14.82 km. This represents a percent change of 20.51% longer for the optimized routes compared to the direct desire lines. The interactive map above visualizes these routes, with desire lines colored based on their lengths and Open Street Routing Machine (OSRM) routes similarly colored with a different theme.

Discussion

The results indicate that the optimized OSRM routes are significantly longer than the direct desire lines, which is generally expected given the constraints of the built environment and road network. The percent change of 20.51% suggests that while the desire lines represent the most direct path between two points, real-world travel must navigate around obstacles, follow roadways, and adhere to traffic regulations etc.

Limitations

• This does not represent all bus stops in NYC, just shelters. Although the exact number of bus stops is difficult to find, the MTA states that there are 327 bus routes in the five boroughs and countless stops in between. To make the data manageable both in computation and visualization, this study only selects 50 at random. This limits the amount of data points and does not fully capture the bus network.
• The OSRM routing service may not always find a route between two points, especially if they are very close together or in areas with limited road connectivity. The code removes these unroutable routes, and they are not shown in the data.
• The analysis does not account for real-world factors such as traffic, hazards, closures, road conditions, bus “bunching” or transit schedules, which can significantly impact actual travel times and route efficiency.The analysis assumes that the shortest path is the most efficient, which may not always be the case in real-world scenarios.
• The sample size of 50 origin-destination pairs is relatively small and is not be representative of the entire bus network in NYC.
• Only “Primary” and “Secondary” roads are sampled here, as the computation for the smaller roads (tertiary etc.) was too processing heavy. This eliminates a large selection of routes.

Future:

Future research could expand the sample size to include more origin-destination pairs, or even all bus stops. Incorporating real-world travel time data, traffic patterns, and transit schedules could provide a more comprehensive understanding of route efficiency. Further analysis could also explore the impact of different modes of transportation, such as cycling or walking, on route optimization and efficiency.

Additional Sources:

https://www.mta.info/agency/new-york-city-transit/subway-bus-facts-2019 https://docs.ropensci.org/stplanr/